Jesse tossed a paint brush off her roof. The height of the brush (in meters above the ground)t seconds after Jesse
tossed it is modeled by
-5+56 + 10
Jesse wants to know when the brush will hit the ground.
1) Rewrite the function in a different form (factored
or vertex) where the answer appears as a number in
the equation.
h(t) =
2) How many seconds after being thrown does the
brush hit the ground?
seconds
PLEASE HELP ASAP

Below

Step-by-step explanation:

1):

-5t^2 + 5t +10 is a qudratic equation so the path created by the tossed paint brush will be a parabola.

● -5t^2 + 5t +10 has the form ax^2 +bx +c

● a = -5

● b = 5

● c = 10

The vertex of this parabola has the coirdinates(-b/2a ; f(-b/2a) )

● -b/2a = -5 / 2×(-5) = 5/10 = 1/2 = 0.5

● f(0.5) = -5×0.5^2 + 5×0.5 +10 = 11.25

So the vertix coordinates are:

● (0.5,11.25)

(Picture below)

The vertex form is:

● a (x-h)^2 + k

● (h,k) are the coordinates of the vertex

So the vertex form of this function is:

● -5(t-0.5)^2 +11.25

■■■■■■■■■■■■■■■■■■■■■■■■■■

2):

The path is a parabola.

Before the brush is thrown the height was 0 and when it hits the ground again it is 0 .

The height is 0 when t reaches the roots of this function.

You can graph the function and extract the roots without calculations.

(-1,0) and (2,0) are the roots.

● 2-(-1) = 2 +1 = 3

So the brush falls after 3 s .

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.